Fusion-Riesz frame in Hilbert space

作     者：LI Xue-bin YANG Shou-zhi 

作者机构：Department of Mathematics Shantou University Shantou 515063 China 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2017年第32卷第3期

页      面：339-352页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(11071152) the Natural Science Foundation of Guangdong Province(S2015A030313443) 

主　　题：fusion-Riesz frame Riesz frame of subspace Riesz frame exact fusion frame 

摘      要：Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some important properties of Riesz frame. In this paper, we show a part of these properties of fusion-Riesz frame and the new results about the stabilities of fusion-Riesz frames under operator perturbation (simple named operator perturbation of fusion-Riesz frames). Moreover, we also compare the operator perturbation of fusion-Riesz frame with that of fusion frame, fusion-Riesz basis (also called Riesz decomposition or Riesz fusion basis) and exact fusion frame.